In this paper, we try to, at first, reveal some key problems, i.e., trapping mechanism, injectivity and leakage risk, for co-injection and co-storage of CO2 and the strong acid SO2 into subsurface spaces in a certain gas field in China. The output of this gas field includes about 6.8 % H2S and 4.6 % CO2. Then, we want to insight into the possibilities and potentials of co-storage of CO2+SO2 by numerical studies. After widely referring all opened and published scientifical and technical literature, we develop a model to study a porous media system associated with the thermo-hydro-chemical coupling interactions. The hydrogeology and mineralogy of the injected formation are extracted from the historical materials of the gas field. We have performed several numerical simulations with consideration of a sandstone-clay sequence under acid-gas injection conditions. The clay formation is supposed as a sealed cap rock for the co-storage disposal system. The study examines the impact of SO2 co-injection on the pH of formation brine. Co-injection of CO2 with SO2 results in a larger and more strongly acidified zone, and alteration differs substantially from that caused by the injection of CO2 alone. The mineral alteration induced by injection of CO2 with SO2 leads to corresponding changes in porosity. Significant increases in porosity occur in the acidified zones where mineral dissolution dominates.